Information needs to be represented in a suitable form in order to be operated upon in a desired way. A coding system is one of such a suitable form. There is not yet a coding system that is good for all purposes and accordingly many coding systems are invented and correspondingly many manipulating in accordance machines are designed. Information represented according to a particular coding system may not be recognized and processed by a machine designed for manipulation according to a different coding system. Communications between one system and another are needed in many cases where code conversion is a must when coding system are not the same. Radix conversion is a very special case limited to number representations where radices are relevant. For example, the conversion of Roman numerals to and from Fibonacci code does not involve radix conversion. Radix conversion according to the conventional methods is equivalent basically to an evaluation of the formula ##EQU1## where N denotes a positive integer needs to be converted and a.sub.i is a digit of a number system of radix r. An evaluation of a formula of such type is not a simple task because it may involve all basic arithmetic operations addition, subtraction, multiplication and division.